Broadband, coherent light carrying optical angular momentum is of potential utility for a variety of classical and quantum communication applications, but at present few such sources exist. We study the generation of supercontinua in a ring array of coupled optical fibres. Short pulses carrying discrete angular momentum undergo soliton fission, spontaneously breaking azimuthal symmetry. This results in a train of pulses with a broadband frequency spectrum as well as a non-trivial angular momentum distribution. These spatio-temporal solitary waves, localised around a single fibre core, emit an unusual form of resonant radiation which can be present even in the absence of intrinsic higher order dispersion, being induced by the lattice dispersion of the ring array. We explore how the coupling properties between fibre cores affect the resulting supercontinuum, in particular how mildly twisting the array can effectively manipulate its angular momentum content and resonant frequencies through the induced Peierls phase.